Centre of Gravity and Equilibrium of Rigid Bodies - Question Bank

1. The center of gravity of a system of particles is the point where:
A) The sum of the masses is concentrated.
B) The sum of the weights is concentrated.
C) The net force is zero.
D) The net torque is zero.
2. If a body is in equilibrium, it means that:
A) It is always at rest.
B) It is either at rest or moving with constant velocity and constant angular velocity.
C) It is always moving with constant velocity.
D) It is always rotating with constant angular velocity.
3. The stability of a body is increased by:
A) Increasing the height of its center of gravity.
B) Decreasing the area of its base of support.
C) Lowering its center of gravity and increasing its base of support.
D) Making it lighter.
4. An object is in neutral equilibrium if its center of gravity:
A) Rises when displaced.
B) Falls when displaced.
C) Remains at the same height when displaced.
D) Is at the lowest possible point.
5. Which of the following is a method to determine the center of gravity of an irregular lamina?
A) Balancing it on a knife-edge.
B) Calculating the geometric center.
C) Measuring its mass.
D) Calculating its volume.
6. For a body to be in equilibrium, the net external torque about any point must be:
A) Zero.
B) Non-zero.
C) Equal to the angular momentum.
D) Equal to the moment of inertia.
7. The condition for equilibrium requires that the vector sum of all forces acting on the body is:
A) Zero.
B) Non-zero.
C) Equal to the weight.
D) Equal to the mass.
8. If the net force on a body is zero, it is in:
A) Rotational equilibrium only.
B) Translational equilibrium.
C) Stable equilibrium.
D) Unstable equilibrium.
9. To make a heavy object easier to lift, one should try to:
A) Lower its center of gravity.
B) Raise its center of gravity.
C) Make its base wider.
D) Make it more dense.
10. A ladder leaning against a wall is generally in a state of:
A) Stable equilibrium.
B) Unstable equilibrium.
C) Neutral equilibrium.
D) Dynamic equilibrium.
11. The center of gravity of a rigid body is independent of:
A) The distribution of mass within the body.
B) The gravitational field.
C) The shape of the body.
D) The external forces acting on it.
12. A body is in static equilibrium. What does this imply?
A) It is at rest and will remain at rest.
B) It is moving with constant velocity.
C) It is rotating with constant angular velocity.
D) It is accelerating linearly.
13. If a body is in rotational equilibrium, what can be said about its angular acceleration?
A) It is always zero.
B) It is constant but not necessarily zero.
C) It can be any value.
D) It is maximum.
14. Which of the following is a unit of moment of force (torque)?
A) Newton (N)
B) Joule (J)
C) Newton-meter (Nm)
D) Pascal (Pa)
15. When does the center of gravity of a non-uniform body lie outside the body itself?
A) Never.
B) Always.
C) For certain shapes and mass distributions.
D) Only when it is in motion.
16. A body is in equilibrium. If an external force is applied, which condition might be violated?
A) Net force is zero.
B) Net torque is zero.
C) Net force is non-zero.
D) Both net force and net torque are zero.
17. What happens to the center of gravity of a body when it is deformed?
A) It remains in the same position.
B) It shifts its position.
C) It disappears.
D) It becomes infinite.
18. If the center of gravity of a body is above the base of support, it will be in equilibrium if:
A) The vertical line through the center of gravity falls inside the base.
B) The vertical line through the center of gravity falls outside the base.
C) The body is rotating.
D) The body is accelerating.
19. The center of gravity of a uniform triangular lamina is at the:
A) Centroid.
B) Circumcenter.
C) Incenter.
D) Orthocenter.
20. The center of gravity of a thin, uniform ring is at its:
A) Outer edge.
B) Inner edge.
C) Center.
D) Any point on its circumference.
21. The center of gravity of a hollow sphere is located at its:
A) Innermost surface.
B) Outermost surface.
C) Center.
D) Any point on its surface.
22. Consider a lever. For it to be in rotational equilibrium, the product of force and its distance from the fulcrum (moment) must satisfy:
A) Sum of clockwise moments = Sum of anticlockwise moments.
B) Sum of clockwise moments > Sum of anticlockwise moments.
C) Sum of clockwise moments < Sum of anticlockwise moments.
D) Net force = 0.
23. A uniform plank is supported at its ends. If a person stands at the center, the plank is in equilibrium. If the person moves towards one end, the plank will:
A) Remain in equilibrium.
B) Tilt down towards the end the person moved to.
C) Tilt up towards the end the person moved to.
D) Rotate about its center.
24. The principle of moments states that for a body in rotational equilibrium:
A) The sum of clockwise moments equals the sum of anticlockwise moments.
B) The sum of clockwise moments is greater than the sum of anticlockwise moments.
C) The sum of clockwise moments is less than the sum of anticlockwise moments.
D) The net force is zero.
25. If a body is in equilibrium, its total kinetic energy must be:
A) Zero.
B) Constant and non-zero.
C) Maximum.
D) Minimum.
26. For a system of particles, the center of gravity coincides with the center of mass if:
A) The gravitational field is uniform.
B) The particles are moving.
C) The particles are stationary.
D) The system is in equilibrium.
27. The sum of moments about a point is zero for a body in:
A) Translational equilibrium only.
B) Rotational equilibrium only.
C) Both translational and rotational equilibrium.
D) No specific type of equilibrium.
28. When a force is applied to a rigid body, it can cause:
A) Only translation.
B) Only rotation.
C) Translation, rotation, or both.
D) Neither translation nor rotation.
29. Which of the following actions would make a tall, narrow object more stable?
A) Raising its center of gravity.
B) Reducing its base of support.
C) Lowering its center of gravity.
D) Increasing its height.
30. Consider a car. To increase its stability, manufacturers typically:
A) Raise the chassis.
B) Widen the wheelbase.
C) Make the car taller.
D) Use lighter materials for the chassis.
31. Lowering the center of gravity of a body tends to:
A) Decrease its stability.
B) Increase its stability.
C) Make it neutrally stable.
D) Make it unstable.
32. A wider base of support generally leads to:
A) Less stability.
B) More stability.
C) No change in stability.
D) Unstable equilibrium.
33. The base of support is defined as the:
A) The area enclosed by the points of contact of the body with the surface.
B) The total surface area of the body.
C) The highest point of the body.
D) The lowest point of the body.
34. If the vertical line passing through the center of gravity falls outside the base of support, the body will:
A) Remain in equilibrium.
B) Be in stable equilibrium.
C) Topple over.
D) Return to its original position.
35. For a body resting on a base, it will be in stable equilibrium as long as its center of gravity remains:
A) Above the base.
B) Below the base.
C) Vertically above the area of support.
D) Vertically below the area of support.
36. When a body is in unstable equilibrium, any slight displacement causes its center of gravity to:
A) Rise.
B) Fall.
C) Remain at the same level.
D) Move horizontally.
37. The condition for a body to be in stable equilibrium is that its center of gravity must be at the:
A) Lowest possible position.
B) Highest possible position.
C) Mid-position.
D) Any position relative to the base.
38. A cone balanced on its vertex is in what type of equilibrium?
A) Stable equilibrium
B) Neutral equilibrium
C) Unstable equilibrium
D) Rotational equilibrium
39. A ball placed on a flat horizontal surface is in what type of equilibrium?
A) Stable equilibrium
B) Neutral equilibrium
C) Unstable equilibrium
D) Static equilibrium
40. What type of equilibrium is achieved when a body, slightly displaced, moves further away from its original position?
A) Stable equilibrium
B) Neutral equilibrium
C) Unstable equilibrium
D) Dynamic equilibrium
41. A ball at the bottom of a hemispherical bowl is in what type of equilibrium?
A) Unstable equilibrium
B) Neutral equilibrium
C) Stable equilibrium
D) Metastable equilibrium
42. What type of equilibrium is achieved when a body, slightly displaced, returns to its original position?
A) Unstable equilibrium
B) Neutral equilibrium
C) Stable equilibrium
D) Absolute equilibrium
43. If a body is suspended from a point, its center of gravity will lie:
A) Vertically above the point of suspension.
B) Vertically below the point of suspension.
C) At the point of suspension.
D) Horizontally from the point of suspension.
44. Consider a uniform rod. Its center of gravity is located at its:
A) One end.
B) Midpoint.
C) One-quarter mark.
D) It depends on how it is held.
45. A body is in equilibrium if it is not accelerating linearly and not accelerating angularly. This means:
A) Its velocity is constant, and its angular velocity is constant.
B) Its acceleration is zero, and its angular acceleration is zero.
C) Its velocity is zero, and its angular velocity is zero.
D) Its acceleration is constant, and its angular acceleration is constant.
46. What is the condition for rotational equilibrium?
A) Sum of all forces is zero.
B) Sum of all torques is zero.
C) Sum of all kinetic energies is zero.
D) Sum of all potentials is zero.
47. What is the condition for translational equilibrium?
A) Sum of all forces is zero.
B) Sum of all torques is zero.
C) Sum of all moments is zero.
D) Sum of all velocities is zero.
48. Which of the following conditions must be met for a rigid body to be in equilibrium?
A) The net force must be zero, and the net torque must be non-zero.
B) The net force must be non-zero, and the net torque must be zero.
C) The net force must be zero, and the net torque must be zero.
D) Both net force and net torque must be non-zero.
49. For a uniform, homogeneous body, where is the center of gravity located?
A) At the point of maximum mass.
B) At the geometric center.
C) At the point farthest from the base.
D) It depends on the external forces acting on it.
50. What is the definition of the center of gravity of a body?
A) The point where all forces acting on the body are applied.
B) The geometric center of the body.
C) The point where the entire weight of the body can be considered to act.
D) The point where the body is most dense.
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